article
Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values
inpress
Fabian
Januszewski
author 81636
We prove new congruences between special values of Rankin-Selberg
$L$-functions for $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$ over arbitrary number
fields. This allows us to control the behavior of $p$-adic $L$-functions under
Tate twists and to prove the existence of non-abelian $p$-adic $L$-functions
for Hida families on $\mathrm{GL}(n+1)\times\mathrm{GL}(n)$. As an application,
we prove strong non-vanishing results for central $L$-values: We give
sufficient local conditions for twisted central Rankin-Selberg $L$-values to be
generically non-zero.
Johns Hopkins University, Johns Hopkins University Press2024
eng
To appear in the American Journal of Mathematics
0002-9327
1708.02616
Januszewski F. Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values. <i>To appear in the American Journal of Mathematics</i>.
F. Januszewski, To Appear in the American Journal of Mathematics (n.d.).
Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions and Non-Vanishing of Central $L$-Values.” <i>To Appear in the American Journal of Mathematics</i>, n.d.
F. Januszewski, “Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values,” <i>To appear in the American Journal of Mathematics</i>.
Januszewski, F. (n.d.). Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values. <i>To Appear in the American Journal of Mathematics</i>.
@article{Januszewski, title={Non-abelian $p$-adic Rankin-Selberg $L$-functions and non-vanishing of central $L$-values}, journal={To appear in the American Journal of Mathematics}, publisher={Johns Hopkins University, Johns Hopkins University Press}, author={Januszewski, Fabian} }
Januszewski, Fabian. “Non-Abelian $p$-Adic Rankin-Selberg $L$-Functions and Non-Vanishing of Central $L$-Values.” <i>To Appear in the American Journal of Mathematics</i>, Johns Hopkins University, Johns Hopkins University Press.
531902024-04-03T16:55:16Z2024-04-03T17:13:33Z